Problem: Simplify the following expression: $ q = \dfrac{-2a}{a + 9} - \dfrac{-9}{7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-2a}{a + 9} \times \dfrac{7}{7} = \dfrac{-14a}{7a + 63} $ Multiply the second expression by $\dfrac{a + 9}{a + 9}$ $ \dfrac{-9}{7} \times \dfrac{a + 9}{a + 9} = \dfrac{-9a - 81}{7a + 63} $ Therefore $ q = \dfrac{-14a}{7a + 63} - \dfrac{-9a - 81}{7a + 63} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-14a - (-9a - 81) }{7a + 63} $ Distribute the negative sign: $q = \dfrac{-14a + 9a + 81}{7a + 63}$ $q = \dfrac{-5a + 81}{7a + 63}$